Solve the quadratic equation by completing the square

HERE IS A PROBLEM FROM MYMATHLAB. I WROTE ALL OF THE DIRECTIONS. AT THE END I SAY WHAT I DON'T UNDERSTAND. PLEASE EXPLAIN IT TO ME AS IF YOU ARE EXPLAINING IT TO A FIVE YEAR OLD.

2x^2+ x- 1/8=0. Solve the quadratic equation by completing the square.
1.)We always begin this process by rearranging the equation so that the constant is on the right side.
2x^2+x= 1/8
2.) Next, divide both sides by 2 so that the coefficient of x^2 is 1.
x^2 + 1/2x= 1/16
3.) Now, find the number that completes the square. To find this number, take the square of half of the coefficient of X. What number will complete the square?
1/16. Now add 1/16 to both sides of the equation.

(x + 1/4)^2 = 1/8

4.)Now take the square root of both sides. The right side will need to be simplified.

x+1/4 = √2/4

Now, solve the equation for x.
x= 1/4 +√2/4

I DON'T UNDERSTAND WHERE THE NUMBER √2/4 CAME FROM. HOW DID THAT COME FROM 1/8? IT SAID TO TAKE THE SQUARE ROOT OF BOTH SIDES. HOW IS √2/4 THE ANSWER FOR 1/8?? IT DOESN'T MAKE ANY SENSE. PLEASE HELP ME